Affinity functions --- the measure of how strongly pairs of adjacent spels in the image hang together ---
represent the core aspect (main
variability parameter) of the fuzzy connectedness (FC) algorithms, an important class of image segmentation schemas.
In this paper, we present the first ever theoretical analysis of the
two standard affinities, homogeneity and object-feature, the way they can be combined, and
which combined versions are truly distinct from each other.
The analysis is based on the notion of equivalent affinities, the theory of which comes from
a companion Part I
of this paper.
We demonstrate that the homogeneity based and object
feature based affinities are equivalent, respectively, to the difference quotient of the intensity function and
Rosenfeld's degree of connectivity.
We also show that many
parameters used in the definitions of these two affinities are
redundant in the sense that changing their values
lead to equivalent affinities.
We finish with an analysis
of possible ways of combining different component affinities
that result in non-equivalent affinities.
In particular, we investigate which of these methods, when applied to
homogeneity based and object-feature based components lead to truly novel (non-equivalent) affinities, and how
this is affected by different choices of parameters.
Since the main goal of the paper is to identify, by formal mathematical arguments,
the affinity functions that are equivalent, extensive experimental confirmations are
not needed --- they show completely identical FC segmentations --- and
as such, only relevant examples of the theoretical results are provided.
Instead, we focus mainly on
theoretical results within a perspective of the
fuzzy connectedness segmentation literature.